CPhill

Here you go :

https://www.mathsisfun.com/pythagoras.html

                    Team Jersey         No Team Jersey        Total

Female              5                         17                            22

Male                 35                          3                            38   

                         40                        20                            60

P(Male / Not wearing a team jersey)    =  3 / 20     =  15%

P(male/ Not wearing a team jersey) is independent if :

P( Male / Not wearing a team jersey)  =  P(Male) * P(Not  wearing a team jersey)

                  .15                   =        38/60 *    20/60 

                  .15      not equal to  .21

So.....not independent

Nice, CU...a "Best Answer ".....!!!!

f(g(x) ) =  A(Bx + A) + B

g(f(x))  =  B(Ax + B) + A

So

f(g(x)) - g (f(x))  =  B - A

[ A(Bx + A) + B  ] - [ B(Ax + B) + A ] =   B - A

 ABx + A^2 + B - ABx - B^2 - A   = B - A

A^2 - B^2 + B - A  = B - A

A^2 - B^2 =  0           factor

(A + B ) ( A - B)  = 0

This implies that  A + B  =  0

Don't know if this helps.....but here are practice questions (with solutions) I found online :

https://www.maa.org/sites/default/files/2017_AMC1012_Practice_Questions.pdf

BTW....GOOD LUCK!!!!!

0 = 5 - 23t - 10t^2      rearrange as

10t^2 + 23t - 5 =  0

Factor as

(5t - 1) ( 2t + 5)  = 0

Setting both factors to 0  and solving for t, we get

t = 1/5 sec = 0.2 sec       or   t = -5/2  sec  =  -2.5 sec

It's obvious that the first answer is correct

6n^2 -18n-18   =  6        subtract 6 from both sides

6n^2 - 18n - 24 =  0          divide each term by 6

n^2 - 3n - 4   = 0

We need two terms that  add to -3   and multiply to   - 4

-4  and 1   seem to do the trick....so...

(n - 4) ( n + 1) = 0

Either

n - 4 = 0            or            n + 1 = 

n = 4                                  n = -1

We have that

a / [ 1 - b]  =  S     (1)      and

b / [ 1 - a ] =  1/S        we can write this as

[ 1 - a ] / b =  S    (2)

Equating (1) and (2)  we have that

a / [ 1 - b ]  =  [ 1 - a ] /  b            cross-multiply

ab = [ 1 - b ] [ 1 - a ]         simplify

ab =  1 - a - b  + ab      subtract ab from both sides

0 = 1 - (a + b)           add (a + b) to both sides

(a + b )   =   1

This is known as a "ceiling" function  shifted down 3 units

The ceiling function basically "rounds up" a value UNLESS that value is already an nteger

Look at the first graph at the top left

The point (1.5, 3)  is on this graph

But Celiing (1.5)  = 2

So

Ceiling (1.5) - 3    =  2 - 3   =  -1

So  this graph is not correct

Look at the graph at the top right

The point (2, 0) is on the graph

Ceiling 2   = 2

But

Ceiling 2 - 3  =   -1

So....this graph is not correct

Look at the graph at the bottom left

This graph is not correct....the point (0, 2) is on the graph

Ceiling (0) = 0

But

Ceiling (0) - 3  =   -3

So  .....this graph is incorrect

Look at the graph at the bottom right

The point (2, - 1)  is on the graph

Ceiling (2) = 2

So

Ceiling (2) - 3   =   2 - 3   = -1

Also....when x = 3.....y = 0   which is correct

So.....you were correct.....this is the correct graph.....!!!!!

Good job, CalculatorUser....!!!!